Chemical sensors with non-covalent, electrostatic surface modification of graphene

ABSTRACT

Embodiments include chemical sensors, devices and systems including the same, and related methods. In an embodiment, a medical device is provided. The medical device can include a graphene varactor, including a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through electrostatic interactions between a partial positive charge on hydrogen atoms of one or more hydrocarbons of the self-assembled monolayer and a it-electron system of graphene. The self-assembled monolayer can include one or more substituted porphyrins or substituted metalloporphyrins, or derivatives thereof. Other embodiments are also included herein.

This application claims the benefit of U.S. Provisional Application No.62/662,305, filed Apr. 25, 2018, the content of which is hereinincorporated by reference in its entirety.

FIELD

Embodiments herein relate to chemical sensors, devices and systemsincluding the same, and related methods. More specifically, embodimentsherein relate to chemical sensors based on the non-covalent surfacemodification of graphene through electrostatic interactions.

BACKGROUND

The accurate detection of diseases can allow clinicians to provideappropriate therapeutic interventions. The early detection of diseasescan lead to better treatment outcomes. Diseases can be detected usingmany different techniques including analyzing tissue samples, analyzingvarious bodily fluids, diagnostic scans, genetic sequencing, and thelike.

Some disease states result in the production of specific chemicalcompounds. In some cases, volatile organic compounds (VOCs) releasedinto a gaseous sample of a patient can be hallmarks of certain diseases.The detection of these compounds or differential sensing of the same canallow for the early detection of particular disease states.

SUMMARY

In a first aspect, a medical device is included. The medical device caninclude a graphene varactor. The graphene varactor can include agraphene layer and a self-assembled monolayer disposed on an outersurface of the graphene layer through electrostatic interactions betweena partial positive charge on hydrogen atoms of one or more hydrocarbonsof the self-assembled monolayer and a n-electron system of graphene. Theself-assembled monolayer can include one or more substituted porphyrinsor substituted metalloporphyrins, or derivatives thereof.

In a second aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can provide a Langmuir theta value of at least0.9.

In a third aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can provide a Langmuir theta value of at least0.98.

In a fourth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can include substituted porphyrins of theformula:

where each R¹ functional group can independently include: —H; —X, whereX is a halogen atom; any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl,C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR, —ZRZR, or—RZRZR, where R can include, but not be limited to, any identical ordifferent, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or any combination thereof, and Z can be one or more heteroatomselected from N, O, P, S, Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR,—RSR, —RCHO, —RX, —RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR,—RNRR, —RB(OH)₂, or any combination thereof, where R can include anyidentical or different, linear, branched, or cyclic C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, or can be absent suchthat the remaining portion of the functional group is covalently bounddirectly to one or more carbon atoms of the substituted porphyrin; and

where each R² and R³ functional group are independently: —H; any linearor branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl or anycombination thereof; —RZR or —RZRZR, where R can include any identicalor different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or any combination thereof, and Z can be one or more heteroatomselected from N, O, P, S, Se, or Si; an aryl, heteroaryl, substitutedaryl, or substituted heteroaryl; a biphenyl or substituted biphenyl; anaryloxy, arylthio, arylamine, or any substitutions thereof; or anycombination thereof; and where R¹, R², and R³ are each covalently bounddirectly to the substituted porphyrin.

In a fifth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the R² and R³functional groups are different than each other.

In a sixth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, each alkyl,alkenyl, alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynylfunctional group can independently include any linear or branchedhydrocarbon functional group having from 6 to 32 carbon atoms (C₆-C₃₂).

In a seventh aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can include substituted porphyrins of theformula:

where each X is independently a heteroatom selected from N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; and

where each R functional group can independently include: —H; any linearor branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof.

In an eighth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can include substituted porphyrins of theformula:

In a ninth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can include substituted metalloporphyrins ofthe formula:

where each R¹ functional group can independently include —H; —X, where Xis a halogen atom; any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl,C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀heteroalkynyl, or any combination thereof; —RZR, —ZRZR, or —RZRZR, whereR can include any identical or different, linear or branched, C₁-C₅₀alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Zcan be one or more heteroatom selected from N, O, P, S, Se, or Si; —ROH,—RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂, —RC(O)NR, —RNH₃⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or any combination thereof,where R can include any identical or different, linear, branched, orcyclic C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combinationthereof, or is absent such that the remaining portion of the functionalgroup is covalently bound directly to one or more carbon atoms of thesubstituted metalloporphyrin; and

where each R² and R³ functional group can independently include: —H; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where R¹, R², and R³ are each covalently bound directly to thesubstituted metalloporphyrin; and

where M is a metal, including, but not limited to, aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and where an oxidation state ofthe metal can include, but not be limited to an oxidation state of I,II, III, IV, V, VI, VII, or VIII. Various inorganic, organic, ionic, orneutral ligands can be coordinated with the metals herein, including,but not to be limited to, Cl⁻, F⁻, Br⁻, I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO,CH₃NH₂, pyridine, and the like. The number of ligands can be from zeroligands to eight ligands.

In a tenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can include substituted metalloporphyrins ofthe formula:

where each X is independently a heteroatom selected from N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; and

where each R functional group can independently include: —H; any linearor branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and where M is ametal including, but not limited to, aluminum, calcium, magnesium,manganese, iron, cobalt, nickel, zinc, ruthenium, palladium, silver,platinum, indium, tin, copper, rhodium, chromium, gallium, osmium,iridium, or derivatives thereof; and where an oxidation state of themetal include, but not be limited to an oxidation state of I, II, III,IV, V, VI, VII, or VIII. Various inorganic, organic, ionic, or neutralligands can be coordinated with the metals herein, including, but not tobe limited to, Cl⁻, F⁻, Br⁻, I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂,pyridine, and the like. The number of ligands can be from zero ligandsto eight ligands.

In an eleventh aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can provide coverage over the graphene from 50%to 150% by surface area.

In a twelfth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, theself-assembled monolayer can provide coverage over the graphene from 99%to 120% by surface area.

In a thirteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, a method ofmodifying a surface of graphene to create a graphene varactor isincluded. The method can include forming a self-assembled monolayerdisposed on an outer surface of a graphene layer through electrostaticinteractions between a partial positive charge on hydrogen atoms of oneor more hydrocarbons of the self-assembled monolayer and a it-electronsystem of graphene. The self-assembled monolayer of the method caninclude one or more substituted porphyrins or substitutedmetalloporphyrins. The method can include quantifying the extent ofsurface coverage of the self-assembled monolayer using contact anglegoniometry, Raman spectroscopy, or X-Ray photoelectron spectroscopy.

In a fourteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the step ofselecting derivatized graphene layers can include selecting derivatizedgraphene layers that exhibit a Langmuir theta value of at least 0.9.

In a fifteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the step ofselecting derivatized graphene layers can include selecting derivatizedgraphene layers that exhibit a Langmuir theta value of at least 0.98.

In a sixteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, a method fordetecting an analyte is included. The method can include collecting agaseous sample from a patient. The method can include contacting agraphene reactor, as described herein.

In a seventeenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the medicaldevice can include a plurality of graphene varactors configured in anarray on the medical device.

In an eighteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, a method fordetecting an analyte is included. The method can include collecting agaseous sample from a patient and contacting the gaseous sample with oneor more graphene varactors. Each of the one or more graphene varactorscan include a graphene layer and a self-assembled monolayer disposed onan outer surface of the graphene layer through electrostaticinteractions between a partial positive charge on hydrogen atoms of oneor more hydrocarbons of the self-assembled monolayer and a it-electronsystem of graphene. The self-assembled monolayer can include at leastone selected from substituted porphyrins or substitutedmetalloporphyrins, or derivatives thereof, as described herein.

In a nineteenth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the method caninclude measuring a differential response in an electrical property ofthe one or more graphene varactors due to the binding of one or moreanalytes present in the gaseous sample.

In a twentieth aspect, in addition to one or more of the preceding orfollowing aspects, or in the alternative to some aspects, the method caninclude the step of measuring an electrical property selected from thegroup including capacitance or resistance.

This summary is an overview of some of the teachings of the presentapplication and is not intended to be an exclusive or exhaustivetreatment of the present subject matter. Further details are found inthe detailed description and appended claims. Other aspects will beapparent to persons skilled in the art upon reading and understandingthe following detailed description and viewing the drawings that form apart thereof, each of which is not to be taken in a limiting sense. Thescope herein is defined by the appended claims and their legalequivalents.

BRIEF DESCRIPTION OF THE FIGURES

Aspects may be more completely understood in connection with thefollowing drawings, in which:

FIG. 1 is a schematic perspective view of a graphene varactor inaccordance with various embodiments herein.

FIG. 2 is a schematic cross-sectional view of a portion of a graphenevaractor in accordance with various embodiments herein.

FIG. 3 is a schematic top plan view of a chemical sensor element inaccordance with various embodiments herein.

FIG. 4 is a schematic diagram of a portion of a measurement zone inaccordance with various embodiments herein.

FIG. 5 is a circuit diagram of a passive sensor circuit and a portion ofa reading circuit in accordance with various embodiments herein.

FIG. 6 is a schematic view of a system for sensing gaseous analytes inaccordance with various embodiments herein.

FIG. 7 is a schematic view of a system for sensing gaseous analytes inaccordance with various embodiments herein.

FIG. 8 is a schematic cross-sectional view of a portion of a chemicalsensor element in accordance with various embodiments herein.

FIG. 9 is a reaction pathway for the synthesis of porphyrin derivativesin accordance with various embodiments herein.

FIG. 10 is a representative plot of relative surface coverage as afunction of concentration in accordance with various embodiments herein.

FIG. 11 is a representative plot of relative surface coverage as afunction of the logarithm of concentration presented in FIG. 10, inaccordance with various embodiments herein.

FIG. 12 is a representative high-resolution XPS spectrum and fits inaccordance with various embodiments herein.

FIG. 13 is a representative high-resolution XPS spectrum in accordancewith various embodiments herein.

While embodiments are susceptible to various modifications andalternative forms, specifics thereof have been shown by way of exampleand drawings, and will be described in detail. It should be understood,however, that the scope herein is not limited to the particularembodiments described. On the contrary, the intention is to covermodifications, equivalents, and alternatives falling within the spiritand scope herein.

DETAILED DESCRIPTION

Embodiments herein relate to chemical sensors, medical devices andsystems including the same, and related methods for detecting chemicalcompounds in gaseous samples, such as, but not limited to, the breath ofa patient. In some embodiments, the chemical sensors herein can be basedon the non-covalent surface modification of graphene with substitutedporphyrins or substituted metalloporphyrins.

Graphene is a form of carbon containing a single layer of carbon atomsin a hexagonal lattice. Graphene has a high strength and stability dueto its tightly packed sp² hybridized orbitals, where each carbon atomforms one sigma (G) bond each with its three neighboring carbon atomsand has one p orbital projected out of the hexagonal plane. The porbitals of the hexagonal lattice can hybridize to form a π band on thesurface of graphene that is suitable for non-covalent electrostaticinteraction and π-π stacking interactions with other molecules.

Porphyrins are a group of heterocyclic macrocycles having four modifiedpyrrole subunits, each connected by a methine (═CH—) bridge. The basiccore structure of an unsubstituted porphyrin is called porphine, whichhas 18 π-electrons that creates a continuous aromatic cycle about themolecule. The structure of porphine, showing its 18 π-electron cycle inbold, is as follows:

Porphyrins can further exist complexed with a metal ion or derivativethereof to form a metalloporphyrin.

Porphyrins or metalloporphyrins substituted, for example, with one ormore alkyl groups can form a well-ordered, non-covalently boundmonolayer on the surface of graphene, where the density of substitutedporphyrins or substituted metalloporphyrins is maximized, and thesubstituted porphyrins or substituted metalloporphyrins are adsorbedonto the surface of the graphene in highly ordered pattern similar to atwo-dimensional crystal.

Without wishing to be bound by any particular theory, it is believedthat hydrogen atoms within hydrocarbon groups (e.g., alkyl chains) caninteract with the nt electron system on the surface of graphene throughelectrostatic interactions. Hydrogen atoms have low electronegativity,and as such, they carry a partial positive charge. The partial positivecharge on the hydrogen atoms of alkyl chains can participate inelectrostatic interactions with the nt electron system of the it band onthe surface of graphene. The alkyl chains can adsorb onto the graphenesurface in an all trans conformation along the carbon-carbon backbone,such that all carbon atoms fall into one plane that is eitherperpendicular or parallel to the graphene surface.

By way of example, the trans conformation of an alkyl chain having aperpendicular orientation of its carbon-carbon backbone along thesurface of graphene creates a configuration where every second —CH₂—group of the alkyl chain has its hydrogen atoms pointing towards thegraphene. As such, alkyl chains can orient themselves with respect tothe graphene surface so that the —CH₂— hydrogens of alternate —CH₂—groups are disposed the same distance from the graphene surface and thehydrogen-graphene interactions are maximized. Thus, the alkyl chain caninteract with the surface of graphene along the length of the alkylchain. It is also believed that the hydrogen atoms of alkenyl chains andalkynyl chains, and derivatives thereof, can similarly interact with thegraphene surface.

The non-covalent functionalization of graphene with a self-assembledmonolayer of porphyrins or metalloporphyrins substituted with, forexample, hydrocarbon groups, does not significantly affect the atomicstructure of graphene, and provides a stable graphene-based sensor withhigh sensitivity towards a number of volatile organic compounds (VOCs)in the parts-per-billion (ppb) or parts-per-million (ppm) levels. Assuch, the embodiments herein can be used to detect VOCs and/ordifferential binding patterns of the same that, in turn, can be used toidentify disease states.

Referring now to FIG. 1, a schematic view of a graphene-based variablecapacitor (or graphene varactor) 100 is shown in accordance with theembodiments herein. It will be appreciated that graphene varactors canbe prepared in various ways with various geometries, and that thegraphene varactor shown in FIG. 1 is just one example in accordance withthe embodiments herein.

Graphene varactor 100 can include an insulator layer 102, a gateelectrode 104 (or “gate contact”), a dielectric layer (not shown in FIG.1), one or more graphene layers, such as graphene layers 108 a and 108b, and a contact electrode 110 (or “graphene contact”). In someembodiments, the graphene layer(s) 108 a-b can be contiguous, while inother embodiments the graphene layer(s) 108 a-b can be non-contiguous.Gate electrode 104 can be deposited within one or more depressionsformed in insulator layer 102. Insulator layer 102 can be formed from aninsulative material such as silicon dioxide, formed on a siliconsubstrate (wafer), and the like. Gate electrode 104 can be formed by anelectrically conductive material such as chromium, copper, gold, silver,nickel, tungsten, aluminum, titanium, palladium, platinum, iridium, andany combinations or alloys thereof, which can be deposited on top of orembedded within the insulator layer 102. The dielectric layer can bedisposed on a surface of the insulator layer 102 and the gate electrode104. The graphene layer(s) 108 a-b can be disposed on the dielectriclayer. The dielectric layer will be discussed in more detail below inreference to FIG. 2.

Graphene varactor 100 includes eight gate electrode fingers 106 a-106 h.It will be appreciated that while graphene varactor 100 shows eight gateelectrode fingers 106 a-106 h, any number of gate electrode fingerconfigurations can be contemplated. In some embodiments, an individualgraphene varactor can include fewer than eight gate electrode fingers.In some embodiments, an individual graphene varactor can include morethan eight gate electrode fingers. In other embodiments, an individualgraphene varactor can include two gate electrode fingers. In someembodiments, an individual graphene varactor can include 1, 2, 3, 4, 5,6, 7, 8, 9, 10, or more gate electrode fingers.

Graphene varactor 100 can include one or more contact electrodes 110disposed on portions of the graphene layers 108 a and 108 b. Contactelectrode 110 can be formed from an electrically conductive materialsuch as chromium, copper, gold, silver, nickel, tungsten, aluminum,titanium, palladium, platinum, iridium, and any combinations or alloysthereof. Further aspects of exemplary graphene varactors can be found inU.S. Pat. No. 9,513,244, the content of which is herein incorporated byreference in its entirety.

The graphene varactors described herein can include those in which asingle graphene layer has been surface-modified through non-covalentelectrostatic interactions between graphene and molecules substitutedwith hydrocarbon groups. In some embodiments, the surface of a singlegraphene layer can be surface-modified through non-covalentelectrostatic interactions between graphene and any one of a number ofsubstituted porphyrins or derivatives thereof. In some embodiments, thesurface of a single graphene layer can be surface-modified throughnon-covalent electrostatic interactions between graphene and any one ofa number of substituted metalloporphyrins derivatives thereof. Detailsregarding the graphene varactors and substituted porphyrins orsubstituted metalloporphyrins suitable for use herein will be discussedmore fully below.

Referring now to FIG. 2, a schematic cross-sectional view of a portionof a graphene varactor 200 is shown in accordance with variousembodiments herein. The graphene varactor 200 can include an insulatorlayer 102 and a gate electrode 104 recessed into the insulator layer102. The gate electrode 104 can be formed by depositing an electricallyconductive material in the depression in the insulator layer 102, asdiscussed above in reference to FIG. 1. A dielectric layer 202 can beformed on a surface of the insulator layer 102 and the gate electrode104. In some examples, the dielectric layer 202 can be formed of amaterial, such as, silicon dioxide, aluminum oxide, hafnium dioxide,zirconium dioxide, hafnium silicate, or zirconium silicate.

The graphene varactor 200 can include a single graphene layer 204 thatcan be disposed on a surface of the dielectric layer 202. The graphenelayer 204 can be surface-modified with a self-assembled monolayer 206.The self-assembled monolayer 206 can be formed of a homogenouspopulation of substituted porphyrins or substituted metalloporphyrinsdisposed on an outer surface of the graphene layer 204 throughnon-covalent electrostatic interactions. Exemplary substitutedporphyrins or substituted metalloporphyrins are described more fullybelow. The self-assembled monolayer 206 can provide at least 90% surfacecoverage (by area) of the graphene layer 204. In some embodiments, theself-assembled monolayer 206 can provide at least 95% surface coverageof the graphene layer 204. In other embodiments, the self-assembledmonolayer 206 can provide at least 98% surface coverage of the graphenelayer 204.

In some embodiments, the self-assembled monolayer can provide at least50%, 60%, 70%, 80%, 81%, 82%, 83%, 84%, 85%, 86%, 87%, 88%, 89%, 90%,91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% surface coverage(by area) of the graphene layer. It will be appreciated that theself-assembled monolayer can provide surface coverage falling within arange wherein any of the forgoing percentages can serve as the lower orupper bound of the range, provided that the lower bound of the range isa value less than the upper bound of the range.

In some embodiments, it will be appreciated that the self-assembly ofsubstituted porphyrins or substituted metalloporphyrins on the surfaceof the graphene layer can include the self-assembly into more than amonolayer, such as a multilayer. Multilayers can be detected andquantified by techniques such as scanning tunneling microscopy (STM) andother scanning probe microscopies. References herein to a percentage ofcoverage greater than 100% shall refer to the circumstance where aportion of the surface area is covered by more than a monolayer, such ascovered by two, three or potentially more layers of the compound used.Thus, a reference to 105% coverage herein shall indicate thatapproximately 5% of the surface area includes more than monolayercoverage over the graphene layer. In some embodiments, graphene surfacescan include 101%, 102%, 103%, 104%, 105%, 110%, 120%, 130%, 140%, 150%,or 175% surface coverage of the graphene layer. It will be appreciatedthat multilayer surface coverage of the graphene layer can fall within arange of surface coverages, wherein any of the forgoing percentages canserve as the lower or upper bound of the range, provided that the lowerbound of the range is a value less than the upper bound of the range.For example, ranges of coverage can include, but are not limited to, 50%to 150% by surface area, 80% to 120% by surface area, 90% to 110%, or99% to 120% by surface area.

In some embodiments, the self-assembled monolayers suitable for useherein can provide coverage of the graphene surface with a monolayer asquantified by the Langmuir theta value of at least some minimumthreshold value, but avoid covering the majority of the surface of thegraphene with a multilayer thicker than a monolayer. Details about theLangmuir theta values and determination of thereof for a particularself-assembled monolayer using Langmuir adsorption theory is describedmore fully below. In some embodiments, the self-assembled monolayerssuitable for use herein provide a Langmuir theta value of at least 0.95.In some embodiments, the self-assembled monolayers suitable for useherein provide a Langmuir theta value of at least 0.98. In someembodiments, the self-assembled monolayers can provide a Langmuir thetavalue of at least 0.85, 0.86, 0.87, 0.88, 0.89, 0.90, 0.91, 0.92, 0.93,0.94, 0.95, 0.96, 0.97, 0.98, 0.99, or 1.0. It will be appreciated thatthe self-assembled monolayer can provide a range of Langmuir thetavalues, wherein any of the forgoing Langmuir theta values can serve asthe lower or upper bound of the range, provided that the lower bound ofthe range is a value less than the upper bound of the range.

Referring now to FIG. 3, a schematic top plan view of a chemical sensorelement 300 is shown in accordance with various embodiments herein. Thechemical sensor element 300 can include a substrate 302. It will beappreciated that the substrate can be formed from many differentmaterials. By way of example, the substrate can be formed from silicon,glass, quartz, sapphire, polymers, metals, glasses, ceramics, cellulosicmaterials, composites, metal oxides, and the like. The thickness of thesubstrate can vary. In some embodiments, the substrate has sufficientstructural integrity to be handled without undue flexure that coulddamage components thereon. In some embodiments, the substrate can have athickness of about 0.05 mm to about 5 mm. The length and width of thesubstrate can also vary. In some embodiments, the length (or major axis)can be from about 0.2 cm to about 10 cm. In some embodiments, the length(or major axis) can be from about 20 m to about 1 cm. In someembodiments, the width (perpendicular to the major axis) can be fromabout 0.2 cm to about 8 cm. In some embodiments, the width(perpendicular to the major axis) can be from about 20 m to about 0.8cm. In some embodiments, the graphene-based chemical sensor can bedisposable.

A first measurement zone 304 can be disposed on the substrate 302. Insome embodiments, the first measurement zone 304 can define a portion ofa first gas flow path. The first measurement zone (or gas sample zone)304 can include a plurality of discrete graphene-based variablecapacitors (or graphene varactors) that can sense analytes in a gaseoussample, such as a breath sample. A second measurement zone (orenvironment sample zone) 306, separate from the first measurement zone304, can also be disposed on the substrate 302. The second measurementzone 306 can also include a plurality of discrete graphene varactors. Insome embodiments, the second measurement zone 306 can include the same(in type and/or number) discrete graphene varactors that are within thefirst measurement zone 304. In some embodiments, the second measurementzone 306 can include only a subset of the discrete graphene varactorsthat are within the first measurement zone 304. In operation, the datagathered from the first measurement zone, which can be reflective of thegaseous sample analyzed, can be corrected or normalized based on thedata gathered from the second measurement zone, which can be reflectiveof analytes present in the environment.

In some embodiments, a third measurement zone (drift control or witnesszone) 308 can also be disposed on the substrate. The third measurementzone 308 can include a plurality of discrete graphene varactors. In someembodiments, the third measurement zone 308 can include the same (intype and/or number) discrete graphene varactors that are within thefirst measurement zone 304. In some embodiments, the third measurementzone 308 can include only a subset of the discrete graphene varactorsthat are within the first measurement zone 304. In some embodiments, thethird measurement zone 308 can include discrete graphene varactors thatare different than those of the first measurement zone 304 and thesecond measurement zone 306. Aspects of the third measurement zone aredescribed in greater detail below.

The first measurement zone, the second measurement zone, and the thirdmeasurement zone can be the same size or can be of different sizes. Thechemical sensor element 300 can also include a component 310 to storereference data. The component 310 to store reference data can be anelectronic data storage device, an optical data storage device, aprinted data storage device (such as a printed code), or the like. Thereference data can include, but is not limited to, data regarding thethird measurement zone (described in greater detail below).

In some embodiments, chemical sensor elements embodied herein caninclude electrical contacts (not shown) that can be used to providepower to components on the chemical sensor element 300 and/or can beused to read data regarding the measurement zones and/or data from thestored in component 310. However, in other embodiments there are noexternal electrical contacts on the chemical sensor element 300.

It will be appreciated that the chemical sensor elements embodied hereincan include those that are compatible with passive wireless sensing. Aschematic diagram of a passive sensor circuit 502 and a portion of areading circuit 522 is shown in FIG. 5 and discussed in more detailbelow. In the passive wireless sensing arrangement, the graphenevaractor(s) can be integrated with an inductor such that one terminal ofthe graphene varactor contacts one end of the inductor, and a secondterminal of the graphene varactor contacts a second terminal of theinductor. In some embodiments, the inductor can be located on the samesubstrate as the graphene varactor, while in other embodiments, theinductor could be located in an off-chip location.

Referring now to FIG. 4, a schematic diagram of a portion of ameasurement zone 400 is shown in accordance with various embodimentsherein. A plurality of discrete graphene varactors 402 can be disposedwithin the measurement zone 400 in an array. In some embodiments, achemical sensor element can include a plurality of graphene varactorsconfigured in an array within a measurement zone. In some embodiments,the plurality of graphene varactors can be identical, while in otherembodiments the plurality of graphene varactors can be different fromone another.

In some embodiments, the discrete graphene varactors can beheterogeneous in that they are all different from one another in termsof their binding behavior specificity with regard to a particularanalyte. In some embodiments, some discrete graphene varactors can beduplicated for validation purposes, but are otherwise heterogeneous fromother discrete graphene varactors. Yet in other embodiments, thediscrete graphene varactors can be homogeneous. While the discretegraphene varactors 402 of FIG. 4 are shown as boxes organized into agrid, it will be appreciated that the discrete graphene varactors cantake on many different shapes (including, but not limited to, variouspolygons, circles, ovals, irregular shapes, and the like) and, in turn,the groups of discrete graphene varactors can be arranged into manydifferent patterns (including, but not limited to, star patterns,zig-zag patterns, radial patterns, symbolic patterns, and the like).

In some embodiments, the order of specific discrete graphene varactors402 across the length 412 and width 414 of the measurement zone can besubstantially random. In other embodiments, the order can be specific.For example, in some embodiments, a measurement zone can be ordered sothat the specific discrete graphene varactors 402 for analytes having alower molecular weight are located farther away from the incoming gasflow relative to specific discrete graphene varactors 402 for analyteshaving a higher molecular weight which are located closer to theincoming gas flow. As such, chromatographic effects which may serve toprovide separation between chemical compounds of different molecularweight can be taken advantage of to provide for optimal binding ofchemical compounds to corresponding discrete graphene varactors.

The number of discrete graphene varactors within a particularmeasurement zone can be from about 1 to about 100,000. In someembodiments, the number of discrete graphene varactors can be from about1 to about 10,000. In some embodiments, the number of discrete graphenevaractors can be from about 1 to about 1,000. In some embodiments, thenumber of discrete graphene varactors can be from about 2 to about 500.In some embodiments, the number of discrete graphene varactors can befrom about 10 to about 500. In some embodiments, the number of discretegraphene varactors can be from about 50 to about 500. In someembodiments, the number of discrete graphene varactors can be from about1 to about 250. In some embodiments, the number of discrete graphenevaractors can be from about 1 to about 50.

Each of the discrete graphene varactors suitable for use herein caninclude at least a portion of one or more electrical circuits. By way ofexample, in some embodiments, each of the discrete graphene varactorscan include one or more passive electrical circuits. In someembodiments, the graphene varactors can be included such that they areintegrated directly on an electronic circuit. In some embodiments, thegraphene varactors can be included such that they are wafer bonded tothe circuit. In some embodiments, the graphene varactors can includeintegrated readout electronics, such as a readout integrated circuit(ROIC). The electrical properties of the electrical circuit, includingresistance or capacitance, can change upon binding, such as specificand/or non-specific binding, with a component from a gas sample.

Referring now to FIG. 5, a schematic diagram of a passive sensor circuit502 and a portion of a reading circuit 522 is shown in accordance withvarious aspects herein. In some embodiments, the passive sensor circuit502 can include a metal-oxide-graphene varactor 504 (wherein RSrepresents the series resistance and CG represents the varactorcapacitor) coupled to an inductor 510. Graphene varactors can beprepared in various ways and with various geometries. By way of example,in some aspects, a gate electrode can be recessed into an insulatorlayer as shown as gate electrode 104 in FIG. 1. A gate electrode can beformed by etching a depression into the insulator layer and thendepositing an electrically conductive material in the depression to formthe gate electrode. A dielectric layer can be formed on a surface of theinsulator layer and the gate electrode. In some examples, the dielectriclayer can be formed of a metal oxide such as, aluminum oxide, hafniumdioxide, zirconium dioxide, silicon dioxide, or of another material suchas hafnium silicate or zirconium silicate. A surface-modified graphenelayer can be disposed on the dielectric layer. Contact electrodes canalso be disposed on a surface of the surface-modified graphene layer,also shown in FIG. 1 as contact electrode 110.

Further aspects of exemplary graphene varactor construction can be foundin U.S. Pat. No. 9,513,244, the content of which is herein incorporatedby reference in its entirety.

In various embodiments, the functionalized graphene layer (e.g.,functionalized to include analyte binding receptors), which is part ofthe graphene varactor and thus part of a sensor circuit, such as apassive sensor circuit, is exposed to the gas sample flowing over thesurface of the measurement zone. The passive sensor circuit 502 can alsoinclude an inductor 510. In some embodiments, only a single varactor isincluded with each passive sensor circuit 502. In other embodiments,multiple varactors are included, such as in parallel, with each passivesensor circuit 502.

In the passive sensor circuit 502, the capacitance of the electricalcircuit changes upon binding of an analyte in the gas sample and thegraphene varactor. The passive sensor circuit 502 can function as an LRCresonator circuit, wherein the resonant frequency of the LRC resonatorcircuit changes upon binding with a component from a gas sample.

The reading circuit 522 can be used to detect the electrical propertiesof the passive sensor circuit 502. By way of example, the readingcircuit 522 can be used to detect the resonant frequency of the LRCresonator circuit and/or changes in the same. In some embodiments, thereading circuit 522 can include a reading coil having a resistance 524and an inductance 526. When the sensor-side LRC circuit is at itsresonant frequency, a plot of the phase of the impedance of the readingcircuit versus the frequency has a minimum (or phase dip frequency).Sensing can occur when the varactor capacitance varies in response tobinding of analytes, which changes the resonant frequency, and/or thevalue of the phase dip frequency.

Referring now to FIG. 6, a schematic view of a system 600 for sensinggaseous analytes in accordance with various embodiments herein is shown.The system 600 can include a housing 618. The system 600 can include amouthpiece 602 into which a subject to be evaluated can blow a breathsample. The gaseous breath sample can pass through an inflow conduit 604and pass through an evaluation sample (patient sample) input port 606.The system 600 can also include a control sample (environment) inputport 608. The system 600 can also include a sensor element chamber 610,into which disposable sensor elements can be placed. The system 600 canalso include a display screen 614 and a user input device 616, such as akeyboard. The system can also include a gas outflow port 612. The system600 can also include flow sensors in fluid communication with the gasflow associated with one or more of the evaluation sample input port 606and control sample input port 608. It will be appreciated that manydifferent types of flow sensors can be used. In some embodiments, ahot-wire anemometer can be used to measure the flow of air. In someembodiments, the system can include a CO₂ sensor in fluid communicationwith the gas flow associated with one or more of the evaluation sampleinput port 606 and control sample input port 608.

In various embodiments, the system 600 can also include other functionalcomponents. By way of example, the system 600 can include a humiditycontrol module 640 and/or a temperature control module 642. The humiditycontrol module can be in fluid communication with the gas flowassociated with one or more of the evaluation sample input port 606 andcontrol sample input port 608 in order to adjust the humidity of one orboth gas flow streams in order to make the relative humidity of the twostreams substantially the same in order to prevent an adverse impact onthe readings obtained by the system. The temperature control module canbe in fluid communication with the gas flow associated with one or moreof the evaluation sample input port 606 and control sample input port608 in order to adjust the temperature of one or both gas flow streamsin order to make the temperature of the two streams substantially thesame in order to prevent an adverse impact on the readings obtained bythe system. By way of example, the air flowing into the control sampleinput port can be brought up to 37 degrees Celsius or higher in order tomatch or exceed the temperature of air coming from a patient. Thehumidity control module and the temperature control module can beupstream from the input ports, within the input ports, or downstreamfrom the input ports in the housing 618 of the system 600. In someembodiments, the humidity control module 640 and the temperature controlmodule 642 can be integrated.

In some embodiments (not shown), the control sample input port 608 ofsystem 600 can also be connected to a mouthpiece 602. In someembodiments, the mouthpiece 602 can include a switching airflow valvesuch that when the patient is drawing in breath, air flows from thecontrol sample input port 608 to the mouthpiece, and the system isconfigured so that this causes ambient air to flow across theappropriate control measurement zone (such as the second measurementzone). Then when the patient exhales, the switching airflow valve canswitch so that a breath sample from the patient flows from themouthpiece 602 through the inflow conduit 604 and into the evaluationsample input port 606 and across the appropriate sample (patient sample)measurement zone (such as the first measurement zone) on the disposablesensor element.

In an embodiment, a method of making a chemical sensor element isincluded. The method can include depositing one or more measurementzones onto a substrate. The method can further include depositing aplurality of discrete graphene varactors within the measurement zones onthe substrate. The method can include generating one or more discretegraphene varactors by modifying a surface of a graphene layer withsubstituted porphyrins or substituted metalloporphyrins to form aself-assembled monolayer on an outer surface of the graphene layerthrough electrostatic interactions. The method can include quantifyingthe extent of surface coverage of the self-assembled monolayer usingcontact angle goniometry, Raman spectroscopy, or X-Ray photoelectronspectroscopy. The method can include selecting derivatized graphenelayers that exhibit a Langmuir theta value of at least 0.9, as will bediscussed more fully below. In some embodiments, the method can includeselecting derivatized graphene layers that exhibit a Langmuir thetavalue of at least 0.98. The method can further include depositing acomponent to store reference data onto the substrate. In someembodiments, the measurement zones can all be placed on the same side ofthe substrate. In other embodiments, the measurement zones can be placedonto different sides of the substrate.

In an embodiment, a method of assaying one or more gas samples isincluded. The method can include inserting a chemical sensor elementinto a sensing machine. The chemical sensor element can include asubstrate and a first measurement zone comprising a plurality ofdiscrete graphene varactors. The first measurement zone can define aportion of a first gas flow path. The chemical sensor element canfurther include a second measurement zone separate from the firstmeasurement zone. The second measurement zone can also include aplurality of discrete graphene varactors. The second measurement zonecan be disposed outside of the first gas flow path.

The method can further include prompting a subject to blow air into thesensing machine to follow the first gas flow path. In some embodiments,the CO₂ content of the air from the subject is monitored and samplingwith the disposable sensor element is conducted during the plateau ofCO₂ content, as it is believed that the air originating from the alveoliof the patient has the richest content of chemical compounds foranalysis, such as volatile organic compounds. In some embodiments, themethod can include monitoring the total mass flow of the breath sampleand the control (or environmental) air sample using flow sensors. Themethod can further include interrogating the discrete graphene varactorsto determine their analyte binding status. The method can furtherinclude discarding the disposable sensor element upon completion ofsampling.

Referring now to FIG. 7, a schematic view of a system 700 for sensinggaseous analytes in accordance with various embodiments herein is shown.In this embodiment, the system is in a hand-held format. The system 700can include a housing 718. The system 700 can include a mouthpiece 702into which a subject to be evaluated can blow a breath sample. Thesystem 700 can also include a display screen 714 and a user input device716, such as a keyboard. The system can also include a gas outflow port712. The system can also include various other components such as thosedescribed with reference to FIG. 6 above.

In some embodiments, one of the measurement zones can be configured toindicate changes (or drift) in the chemical sensor element that couldoccur as a result of aging and exposure to varying conditions (such asheat exposure, light exposure, molecular oxygen exposure, humidityexposure, etc.) during storage and handling prior to use. In someembodiments, the third measurement zone can be configured for thispurpose.

Referring now to FIG. 8, a schematic cross-sectional view is shown of aportion of a chemical sensor element 800 in accordance with variousembodiments herein. The chemical sensor element 800 can include asubstrate 802 and a discrete graphene varactor 804 disposed thereon thatis part of a measurement zone. Optionally, in some embodiments thediscrete graphene varactor 804 can be encapsulated by an inert material806, such as nitrogen gas, or an inert liquid or solid. In this manner,the discrete graphene varactor 804 for the third measurement zone can beshielded from contact with gas samples and can therefore be used as acontrol or reference to specifically control for sensor drift which mayoccur between the time of manufacturing and the time of use of thedisposable sensor element. In some embodiments, such as in the case ofthe use of an inert gas or liquid, the discrete binding detector canalso include a barrier layer 808, which can be a layer of a polymericmaterial, a foil, or the like. In some cases, the barrier layer 808 canbe removed just prior to use.

In an embodiment, a method for detecting one or more analytes isincluded. The method can include collecting a gaseous sample from apatient. In some embodiments the gaseous sample can include exhaledbreath. In other embodiments, the gaseous sample can include breathremoved from the lungs of a patient via a catheter or other similarextraction device. In some embodiments, the extraction device caninclude an endoscope, a bronchoscope, or tracheoscope. The method canalso include contacting a graphene varactor with the gaseous sample,where the graphene varactor includes a graphene layer and aself-assembled monolayer disposed on an outer surface of the graphenelayer through electrostatic interactions. In some embodiments, theself-assembled monolayer can provide a Langmuir theta value of at least0.9. In some embodiments, the method can include selecting derivatizedgraphene layers that exhibit a Langmuir theta value of at least 0.98.Langmuir theta values will be discussed more fully below. In someembodiments, the method can include measuring a differential response ina capacitance of the graphene reactor due to the binding of one or moreanalytes present in the gaseous sample, which in turn can be used toidentify disease states. In some embodiments, the method can include aself-assembled monolayer selected from at least one substitutedporphyrin or substituted metalloporphyrin, or derivatives thereof.

Graphene Varactors

The graphene varactors described herein can be used to sense one or moreanalytes in a gaseous sample, such as, for example, the breath of apatient. Graphene varactors embodied herein can exhibit a highsensitivity for volatile organic compounds (VOCs) found in gaseoussamples at or near parts-per-million (ppm) or parts-per-billion (ppb)levels. The adsorption of VOCs onto the surface of graphene varactorscan change the resistance, capacitance, or quantum capacitance of suchdevices, and can be used to detect the VOCs and/or patterns of bindingby the same that, in turn, can be used to identify disease states suchas cancer, cardiac diseases, infections, multiple sclerosis, Alzheimer'sdisease, Parkinson's disease, and the like. The graphene varactors canbe used to detect individual analytes in gas mixtures, as well aspatterns of responses in highly complex mixtures. In some embodiments,one or more graphene varactors can be included to detect the sameanalyte in a gaseous sample. In some embodiments, one or more graphenevaractors can be included to detect different analytes in a gaseoussample. In some embodiments, one or more graphene varactors can beincluded to detect a multitude of analytes in a gaseous sample.

An exemplary graphene varactor can include a graphene layer and aself-assembled monolayer disposed on an outer surface of the graphenelayer, interacting with the latter through electrostatic interactions,as shown and discussed above in reference to FIG. 2. The self-assembledmonolayers suitable for use herein can provide a Langmuir theta value ofat least 0.9. Determination of the Langmuir theta value for a particularself-assembled monolayer using Langmuir adsorption theory is describedmore fully below. In some embodiments, the self-assembled monolayerssuitable for use herein provide a Langmuir theta value of at least 0.95.In some embodiments, the self-assembled monolayers suitable for useherein provide a Langmuir theta value of at least 0.98.

The graphene varactors described herein can include those in which asingle graphene layer has been surface-modified through non-covalentelectrostatic interactions with one or more substituted porphyrins orsubstituted metalloporphyrins, as described elsewhere herein.Substituted porphyrins or substituted metalloporphyrins suitable for useherein can be substituted with any number of functional groups describedbelow, including, but not limited to alkyl groups, alkenyl groups,heteroalkyl groups, heteroalkenyl groups, aryl groups, heteroarylgroups, biphenyl groups, substituted biphenyl groups, substituted arylgroups, and/or substituted heteroaryl groups.

In some embodiments, the substituted porphyrins and substitutedmetalloporphyrins herein can be substituted with any of the followingfunctional groups at anywhere from 1 to 12 positions about the porphyrinor metalloporphyrin ring structure, or more, as is the case for anexpanded substituted porphyrin or expanded substituted metalloporphyrin.In some embodiments, an expanded substituted porphyrin ormetalloporphyrin can be substituted with any of the following functionalgroups at anywhere from 1 to greater than 12 positions about theexpanded substituted porphyrin or expanded substituted metalloporphyrinring structure. In some embodiments, the porphyrin or metalloporphyrinring structure is substituted at only one position about the porphyrinor metalloporphyrin ring structure. In some embodiments, the porphyrinor metalloporphyrin ring structure is substituted at only 2 positionsabout the porphyrin or metalloporphyrin ring structure. In someembodiments, the substituted porphyrins or substituted metalloporphyrinsherein can be substituted at 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12positions about the porphyrin or metalloporphyrin ring structure.

In some embodiments, the substitutions to the porphyrin ormetalloporphyrin ring structures can be symmetrical, whereas in otherembodiments the substitutions to the porphyrin or metalloporphyrin ringstructures can be asymmetrical. Likewise, in some embodiments, thesubstitutions to the expanded substituted porphyrin or expandedsubstituted metalloporphyrin ring structures can be symmetrical, whereasin other embodiments the substitutions to the expanded substitutedporphyrin or expanded substituted metalloporphyrin ring structures canbe asymmetrical

As used herein, the term “alkyl” refers to any linear or branchedhydrocarbon functional group containing anywhere from 1 to 50 carbonatoms (i.e., C₁-C₅₀ alkyl). In some embodiments, the alkyl groups hereincan contain any linear or branched hydrocarbon functional groupcontaining anywhere from 6 to 32 carbon atoms (i.e., C₆-C₃₂ alkyl). Inother embodiments, the alkyl groups herein can contain any linear orbranched hydrocarbon functional group containing anywhere from 12 to 26carbon atoms (i.e., C₁₂-C₂₆ alkyl). The alkyl groups described hereinhave the general formula C_(n)H_(2n+1), unless otherwise indicated.

As used herein, the term “alkenyl” refers to any linear or branchedhydrocarbon functional group containing anywhere from 1 to 50 carbonatoms, wherein the alkenyl group contains at least one carbon-carbondouble bond (i.e., C₁-C₅₀ alkenyl). In some embodiments, the alkenylgroups herein can contain any linear or branched hydrocarbon functionalgroup containing anywhere from 6 to 32 carbon atoms, wherein the alkenylgroup contains at least one carbon-carbon double bond (i.e., C₆-C₃₂alkenyl). In other embodiments, the alkenyl groups herein can containany linear or branched hydrocarbon functional group containing anywherefrom 12 to 26 carbon atoms, wherein the alkenyl group contains at leastone carbon-carbon double bond (i.e., C₁₂-C₂₆ alkenyl). The alkenylgroups described herein have the general formula C_(n)H_((2n+1-2x)),where x is the number of double bonds present in the alkenyl group,unless otherwise indicated.

As used herein, the term “alkynyl” refers to any linear or branchedhydrocarbon functional group containing anywhere from 1 to 50 carbonatoms, including one or more carbon-carbon triple bonds (i.e., C₁-C₅₀alkynyl). In some embodiments, the alkynyl groups herein can contain anylinear or branched hydrocarbon functional group containing anywhere from6 to 32 carbon atoms, including one or more carbon-carbon triple bonds(i.e., C₆-C₃₂ alkynyl). In other embodiments, the alkynyl groups hereincan contain any linear or branched hydrocarbon functional groupcontaining anywhere from 12 to 26 carbon atoms, including one or morecarbon-carbon triple bonds (i.e., C₁₂-C₂₆ alkynyl).

As used herein, the term “heteroalkyl” refers to any linear or branchedhydrocarbon functional group containing anywhere from 1 to 50 carbonatoms, and one or more heteroatoms, including, but not limited to, N, O,P, S, Si, Se, and B, or any combination thereof (i.e., C₁-C₅₀heteroalkyl). In some embodiments, the heteroalkyl groups herein cancontain any linear or branched hydrocarbon functional group containinganywhere from 6 to 32 carbon atoms and one or more heteroatoms,including, but not limited to, N, O, P, S, Si, Se, and B, or anycombination thereof (i.e., C₆-C₃₂ heteroalkyl). In other embodiments,the heteroalkyl groups herein can contain any linear or branchedhydrocarbon functional group containing anywhere from 12 to 26 carbonatoms and one or more heteroatoms, including, but not limited to, N, O,P, S, Si, Se, and B, or any combination thereof (i.e., C₁₂-C₂₆heteroalkyl). In some embodiments, the heteroalkyl groups herein canhave the general formula —RZR, —ZRZR, or —RZRZR, where R can include,but not be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, or a combination thereof; and Z can include one or moreheteroatoms including, but not limited to, N, O, P, S, Si, Se, and B, orany combination thereof.

In some embodiments, the heteroalkyl group can include, but not limitedto, alkoxy groups, alkyl amide groups, alkyl thioether groups, alkylester groups, and the like. Examples of heteroalkyl groups suitable foruse herein can include, but not be limited to, those selected from —ROH,—RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂, —RC(O)NR, —RNH₃⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or any combination thereof;where R can include, but not be limited to, any identical or different,linear or branched, C₁-C₅₀ alkyl, or a combination thereof; and X can bea halogen including F, Cl, Br, I, or At.

As used herein, the term “heteroalkenyl” refers to any linear orbranched hydrocarbon functional group containing anywhere from 1 to 50carbon atoms, including one or more carbon-carbon double bonds, and oneor more heteroatoms including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₁-C₅₀ heteroalkenyl). In someembodiments, the heteroalkenyl groups herein can contain any linear orbranched hydrocarbon functional group containing anywhere from 6 to 32carbon atoms, including one or more carbon-carbon double bonds, and oneor more heteroatoms, including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₆-C₃₂ heteroalkenyl). In otherembodiments, the heteroalkenyl groups herein can contain any linear orbranched hydrocarbon functional group containing anywhere from 12 to 26carbon atoms, including one or more carbon-carbon double bonds, and oneor more heteroatoms, including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₁₂-C₂₆ heteroalkenyl). In someembodiments, the heteroalkenyl groups herein can have the generalformula —RZR, —ZRZR, or —RZRZR, where R can include, but not be limitedto, any identical or different, linear or branched, C₁-C₅₀ alkyl orC₁-C₅₀ alkenyl, provided that at least one carbon-carbon double bond ispresent in at least one R group, or a combination thereof; and Z caninclude one or more heteroatoms including, but not limited to, N, O, P,S, Si, Se, and B, or any combination thereof.

In some embodiments, the heteroalkenyl group can include, but notlimited to, alkenoxy groups, alkenyl amines, alkenyl thioester groups,alkenyl ester groups, and the like. Examples of heteroalkenyl groupssuitable for use herein can include, but not be limited to, thoseselected from —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX,—RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, orany combination thereof; where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkenyl, or acombination thereof; and X can be a halogen including F, Cl, Br, I, orAt.

As used herein, the term “heteroalkynyl” refers to any linear orbranched hydrocarbon functional group containing anywhere from 1 to 50carbon atoms, including one or more carbon-carbon triple bonds, and oneor more heteroatoms including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₁-C₅₀ heteroalkynyl). In someembodiments, the heteroalkynyl groups herein can contain any linear orbranched hydrocarbon functional group containing anywhere from 6 to 32carbon atoms, including one or more carbon-carbon triple bonds, and oneor more heteroatoms, including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₆-C₃₂ heteroalkynyl). In otherembodiments, the heteroalkynyl groups herein can contain any linear orbranched hydrocarbon functional group containing anywhere from 12 to 26carbon atoms, including one or more carbon-carbon triple bonds, and oneor more heteroatoms, including, but not limited to, N, O, P, S, Si, Se,and B, or any combination thereof (i.e., C₁₂-C₂₆ heteroalkynyl). In someembodiments, the heteroalkynyl groups herein can have the generalformula —RZR, —ZRZR, or —RZRZR, where R can include, but not be limitedto, any identical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, or C₁-C₅₀ alkynyl, provided that at least one carbon-carbontriple bond is present in at least one R group or a combination thereof;and Z can include one or more heteroatoms including, but not limited to,N, O, P, S, Si, Se, and B, or any combination thereof.

In some embodiments, the heteroalkynyl group can include, but notlimited to, alkynyloxy groups, alkynyl amines, alkynyl thioester groups,alkynyl ester groups, and the like. Examples of heteroalkynyl groupssuitable for use herein can include, but not be limited to, thoseselected from —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX,—RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, orany combination thereof; where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkynyl, or acombination thereof; and X can be a halogen including F, Cl, Br, I, orAt.

As used herein, the term “biphenyl” refers to an aromatic hydrocarbonfunctional group with the molecular formula (C₆H₅)₂, and when bound to aporphyrin or metalloporphyrin has one less hydrogen at the site ofcovalent attachment to the porphyrin or metalloporphyrin ring structure.In some embodiments, the biphenyl functional group can be substituted toform a substituted biphenyl functional group. As used herein, the term“substituted biphenyl” refers to a biphenyl functional group, asdescribed, which itself is substituted with one or more alkyl, alkenyl,alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynyl functional groups,or any combination thereof, as described herein.

As used herein, the term “aryl” refers to any aromatic hydrocarbonfunctional group containing a C₅- to C₈-membered aromatic ring, such as,for example, cyclopentadiene, benzene, and derivatives thereof. Thecorresponding aromatic radicals to the examples provided include, forexample, cyclopentadienyl and phenyl radicals, and derivatives thereof.In some embodiments, the aryl functional groups herein can be furthersubstituted to form substituted aryl functional groups. As used herein,the term “substituted aryl” refers to any aromatic hydrocarbonfunctional group containing a C₅- to C₈-membered aromatic ring, whichitself can be substituted with one or more alkyl, alkenyl, alkynyl,heteroalkyl, heteroalkenyl, or heteroalkynyl functional groups, or anycombination thereof, as described herein.

In some embodiments, the aryl functional groups herein can besubstituted to form aryloxy functional groups. As used herein, the term“aryloxy” can include a functional group of the general formula Aryl-O—,where the aryl functional group can include a C₅- to C₈-memberedaromatic ring. In some embodiments, the aryloxy group can include aphenoxy functional group of the formula C₆H₅O—. In some embodiments, thearyloxy functional group can be further substituted. As used herein, theterm “substituted aryloxy” can include any aryloxy functional group, asdefined herein, which is further substituted with one or more alkyl,alkenyl, alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynylfunctional groups, or any combination thereof, as described herein.

In some embodiments, the aryl functional groups herein can besubstituted to form arylthio functional groups. As used herein, the term“arylthio” can include a functional group of the general formulaAryl-S—, where the aryl functional group can include a C₅- toC₈-membered aromatic ring. In some embodiments, the arylthio functionalgroup can include a phenylsulfanyl functional group of the formulaC₆H₅S—. In some embodiments, the arylthio functional group can befurther substituted. As used herein, the term “substituted arylthio” caninclude any arylthio functional group, as defined herein, which isfurther substituted with one or more alkyl, alkenyl, alkynyl,heteroalkyl, heteroalkenyl, or heteroalkynyl functional groups, or anycombination thereof, as described herein.

In some embodiments, the aryl functional groups herein can besubstituted to form arylamine functional groups. As used herein, theterm “arylamine” can include a functional group of the general formulaAryl-NH_(n), where the aryl functional group can include a C₅- toC₈-membered aromatic ring, and n can be from 0 to 3, providing that whenn=0, 1, or 2, a non-H substitution is present on the N atom, which caninclude, but is not to be limited to, one or more alkyl, alkenyl,alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynyl functional groups,or any combination thereof, as described herein.

In some embodiments, the arylamine functional group can include aλ¹-azanylbenzene functional group of the formula C₆H₅N. In someembodiments, the arylamine functional group can be further substituted.As used herein, the term “substituted arylamine” can include anyarylamine functional group, as defined herein, which is furthersubstituted with one or more alkyl, alkenyl, alkynyl, heteroalkyl,heteroalkenyl, or heteroalkynyl functional groups, or any combinationthereof, as described herein.

In some embodiments, the aryl functional groups herein can include oneor more heteroatoms to form heteroaryl functional groups. Suitableheteroatoms for use herein can include, but not be limited to, N, O, P,S, Si, Se, and B. As used herein, the term “heteroaryl” refers to anyaryl functional group, as defined herein, where one or more carbon atomsof the C₅- to C₈-membered aromatic ring has been replaced with one ormore heteroatoms or combinations of heteroatoms. Examples of heteroarylfunctional groups can include, but not be limited to radicals of,pyrrole, thiophene, furan, imidazole, pyridine, and pyrimidine. Theheteroaryl functional groups herein can be further substituted to formsubstituted heteroaryl functional groups. As used herein, the term“substituted heteroaryl” refers to any heteroaryl functional group, asdescribed herein, which is further substituted with one or more alkyl,alkenyl, alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynylfunctional groups, or any combination thereof, as described herein.

In some embodiments, the substituted porphyrins herein can include thosehaving the general formula (1):

where each R¹ is independently —H; —X, where X is a halogen atom; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include, butnot be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or any combinationthereof, and Z can be one or more heteroatom selected from N, O, P, S,Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂,—RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or anycombination thereof, where R can include, but is not to be limited to,any identical or different, linear, branched, or cyclic C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, or can beabsent such that the remaining portion of the functional group iscovalently bound directly to one or more carbon atoms of the substitutedporphyrin; and

where each R² and R³ are independently —H; any linear or branched C₁-C₅₀alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR or—RZRZR, where R can include, but not be limited to, any identical ordifferent, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or any combination thereof, and Z can be one or more heteroatomselected from N, O, P, S, Se, or Si; an aryl, heteroaryl, substitutedaryl, or substituted heteroaryl; a biphenyl or substituted biphenyl; anaryloxy, arylthio, arylamine, or any substitutions thereof; or anycombination thereof; and

where every R¹, R², and R³ group is covalently bound directly to thesubstituted porphyrin.

In some embodiments, the R² and R³ groups are the same, while in otherembodiments the R² and R³ groups are different.

In some embodiments, the substituted porphyrins can include those havingthe general formula (2):

where each X is independently a heteroatom selected from N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; and

where each R is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof.

In some embodiments, the substituted porphyrins can include those havingthe general formula (3):

where each X is independently a heteroatom, including, but not limitedto N, O, P, S, Se, or Si; and

where each R is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or one R group can be absent; or any combinationthereof.

In some embodiments, suitable substituted porphyrins for use herein caninclude those having formulas (4) through (9) as shown in TABLE 1.

TABLE 1 Substituted Porphyrins

(4)

(5)

(6)

(7)

(8)

(9)

In some embodiments, the substituted porphyrins can include those havingphthalocyanine substitutions in the place of one or more of the pyrrolesubunits of the porphyrin ring structure of formula (1). Thephthalocyanine-substituted porphyrins suitable for use herein includethose having the general formulas (10) through (14), as shown in TABLE2.

TABLE 2 Phthalocyanine-substituted porphyrins

(10)

(11)

(12)

(13)

(14)

where each R¹ and R⁴ are independently —H; —X, where X is a halogenatom; any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl,or any combination thereof; —RZR, —ZRZR, or —RZRZR, where R can include,but not be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, or C₁-C₅₀ alkynyl, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; —ROH, —RC(O)OH,—RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂,—RNO₂, —RNR, —RNRR, —RB(OH)₂, or any combination thereof, where R caninclude, but is not to be limited to, any identical or different,linear, branched, or cyclic C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or a combination thereof, or can be absent such that theremaining portion of the functional group is covalently bound directlyto one or more carbon atoms of the phthalocyanine-substituted porphyrin;and where R² and R³ are independently —H; any linear or branched C₁-C₅₀alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where every R¹, R², R³, and R⁴ group is covalently bound directly to thephthalocyanine-substituted porphyrin.

In some embodiments, the R² and R³ groups are the same, while in otherembodiments the R² and R³ groups are different.

In some embodiments, the substituted porphyrins herein can include oneor more expanded substituted porphyrins. As used herein, the term“expanded substituted porphyrin” refers to a porphyrin having anexpanded ring structure including more than the four pyrrole ringsassociated with the structure shown in formula (1). In some embodiments,the expanded substituted porphyrin can include 5 modified pyrrolesubunits, each connected by a methine (═CH—) bridge. In someembodiments, the expanded substituted porphyrin ring structure caninclude 6 modified pyrrole subunits, each connected by a methine (═CH—)bridge. In some embodiments, the expanded substituted porphyrin ringstructure can include more than 6 modified pyrrole subunits, eachconnected by a methine (═CH—) bridge. Exemplary expanded substitutedporphyrin molecules include, but are not to be limited to, thoseexpanded substituted porphyrin molecules having the general formulas(15) and (16) as shown in TABLE 3.

TABLE 3 Expanded Substituted Porphyrins

(15)

(16)

where each R¹ is independently —H; —X, where X is a halogen atom; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include, butnot be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or any combinationthereof, and Z can be one or more heteroatom selected from N, O, P, S,Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂,—RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or anycombination thereof, where R can include, but is not to be limited to,any identical or different, linear, branched, or cyclic C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, or can beabsent such that the remaining portion of the functional group iscovalently bound directly to one or more carbon atoms of the expandedsubstituted porphyrin; and

where R² is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR or—RZRZR, where R can include, but not be limited to, any identical ordifferent, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or any combination thereof, and Z can be one or more heteroatomselected from N, O, P, S, Se, or Si; an aryl, heteroaryl, substitutedaryl, or substituted heteroaryl; a biphenyl or substituted biphenyl; anaryloxy, arylthio, arylamine, or any substitutions thereof; or anycombination thereof; and

where every R¹ are R² groups are covalently bound directly to theexpanded substituted porphyrin.

It will be appreciated that the expanded substituted porphyrin ringstructures described herein can further include those havingphthalocyanine substitutions in the place of one or more of the pyrrolesubunits of the porphyrin ring structures of formulas (15) and (16).

In some embodiments, the graphene varactors described herein can includethose in which a single graphene layer has been surface-modified throughnon-covalent electrostatic interactions between the graphene layer andsubstituted metalloporphyrins. In some embodiments, the substitutedmetalloporphyrins herein can include those having the general formula(17):

where each R¹ is independently —H; —X, where X is a halogen atom; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include, butnot be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or any combinationthereof, and Z can be one or more heteroatom selected from N, O, P, S,Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂,—RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or anycombination thereof, where R can include, but is not to be limited to,any identical or different, linear, branched, or cyclic C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, or can beabsent such that the remaining portion of the functional group iscovalently bound directly to one or more carbon atoms of the substitutedmetalloporphyrin; and

where R² and R³ are independently —H; any linear or branched C₁-C₅₀alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where every R¹, R², and R³ group is covalently bound directly to thesubstituted metalloporphyrin; and

where M is a metal including but not limited to aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and where the oxidation stateof the metal can include, but not be limited to an oxidation state of I,II, III, IV, V, VI, VII, or VIII. In some embodiments, the metal ismagnesium. In some embodiments the metal is silver. In some embodimentsthe metal is platinum. In some embodiments the metal is palladium. Insome embodiments the metal is zinc. In some embodiments, variousinorganic, organic, ionic, or neutral ligands can be coordinated withthe metals herein, including, but not to be limited to, Cl⁻, F⁻, Br⁻,I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, and the like. In someembodiments, the number of ligands can be from zero ligands to eightligands.

In some embodiments, the R² and R³ groups are the same, while in otherembodiments the R² and R³ groups are different.

In some embodiments, the substituted metalloporphyrins can include thosehaving the general formula (18):

where each X is independently a heteroatom selected from N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; and

where each R is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where M is a metal including but not limited to aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and where the oxidation stateof the metal can include, but not be limited to an oxidation state of I,II, III, IV, V, VI, VII, or VIII. In some embodiments, the metal ismagnesium. In some embodiments the metal is silver. In some embodimentsthe metal is platinum. In some embodiments the metal is palladium. Insome embodiments the metal is zinc. In some embodiments, variousinorganic, organic, ionic, or neutral ligands can be coordinated withthe metals herein, including, but not to be limited to, Cl⁻, F⁻, Br⁻,I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, and the like. In someembodiments, the number of ligands can be from zero ligands to eightligands.

In some embodiments, the substituted metalloporphyrins can include thosehaving the general formula (19):

where each X is independently a heteroatom selected from N, O, P, S, Se,or Si; and

where each R is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or one R group can be absent; or any combinationthereof; and where M is a metal including but not limited to aluminum,calcium, magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium,palladium, silver, platinum, indium, tin, copper, rhodium, chromium,gallium, osmium, iridium, or derivatives thereof; and where theoxidation state of the metal can include, but not be limited to anoxidation state of I, II, III, IV, V, VI, VII, or VIII. In someembodiments, the metal is magnesium. In some embodiments the metal issilver. In some embodiments the metal is platinum. In some embodimentsthe metal is palladium. In some embodiments the metal is zinc. In someembodiments, various inorganic, organic, ionic, or neutral ligands canbe coordinated with the metals herein, including, but not to be limitedto, Cl⁻, F⁻, Br⁻, I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, andthe like. In some embodiments, the number of ligands can be from zeroligands to eight ligands.

In some embodiments, suitable substituted metalloporphyrins can includethose having formulas (20) through (25) as shown in TABLE 4.

TABLE 4 Substituted Metalloporphyrins

(20)

(21)

(22)

(23)

(24)

(25)

In the embodiments shown in formulas (20) through (25), M is a metalincluding but not limited to aluminum, calcium, magnesium, manganese,iron, cobalt, nickel, zinc, ruthenium, palladium, silver, platinum,indium, tin, copper, rhodium, chromium, gallium, osmium, iridium, orderivatives thereof; and where the oxidation state of the metal caninclude, but not be limited to an oxidation state of I, II, III, IV, V,VI, VII, or VIII. In some embodiments, the metal is magnesium. In someembodiments the metal is silver. In some embodiments the metal isplatinum. In some embodiments the metal is palladium. In someembodiments the metal is zinc. In some embodiments, various inorganic,organic, ionic, or neutral ligands can be coordinated with the metalsherein, including, but not to be limited to, Cl⁻, F⁻, Br⁻, I⁻, CN⁻,SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, and the like. In someembodiments, the number of ligands can be from zero ligands to eightligands.

In some embodiments, the substituted metalloporphyrins can include thoseincluding phthalocyanine substitutions in the place of one or more ofthe pyrrole subunits of the metalloporphyrin ring structure of formula(17). The phthalocyanine-substituted metalloporphyrins include thosehaving the general formulas (26) through (30), as shown in TABLE 5.

TABLE 5 Phthalocyanine-substituted metalloporphyrins

(26)

(27)

(28)

(29)

(30)

where each R¹ and R⁴ are independently —H; —X, where X is a halogenatom; any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl,or any combination thereof; —RZR, —ZRZR, or —RZRZR, where R can include,but not be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or any combinationthereof, and Z can be one or more heteroatom selected from N, O, P, S,Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂,—RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or anycombination thereof, where R can include, but is not to be limited to,any identical or different, linear, branched, or cyclic C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combination thereof, or can beabsent such that the remaining portion of the functional group iscovalently bound directly to one or more carbon atoms of thephthalocyanine-substituted metalloporphyrin; and

where R² and R³ are independently —H; any linear or branched C₁-C₅₀alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where every R¹, R², R³, and R⁴ group is covalently bound directly to thephthalocyanine-substituted metalloporphyrin; and

where M is a metal including but not limited to aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and where the oxidation stateof the metal can include, but not be limited to an oxidation state of I,II, III, IV, V, VI, VII, or VIII. In some embodiments, the metal ismagnesium. In some embodiments the metal is silver. In some embodimentsthe metal is platinum. In some embodiments the metal is palladium. Insome embodiments the metal is zinc. In some embodiments, variousinorganic, organic, ionic, or neutral ligands can be coordinated withthe metals herein, including, but not to be limited to, Cl⁻, F⁻, Br⁻,I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, and the like. In someembodiments, the number of ligands can be from zero ligands to eightligands.

In some embodiments, the R² and R³ groups are the same, while in otherembodiments the R² and R³ groups are different.

In some embodiments, the substituted metalloporphyrins herein caninclude one or more expanded substituted metalloporphyrins. As usedherein, the term “expanded substituted metalloporphyrin” refers to ametalloporphyrin having an expanded ring structure including more thanthe four pyrrole rings associated with the structure shown in formula(11). In some embodiments, the expanded substituted metalloporphyrin caninclude 5 modified pyrrole subunits, each connected by a methine (═CH—)bridge. In some embodiments, the expanded substituted metalloporphyrinring structure can include 6 modified pyrrole subunits, each connectedby a methine (═CH—) bridge. In some embodiments, the expandedsubstituted metalloporphyrin ring structure can include more than 6modified pyrrole subunits, each connected by a methine (═CH—) bridge.Exemplary expanded substituted metalloporphyrin molecules include, butare not to be limited to, those expanded substituted metalloporphyrinmolecules having the general formulas (9) and (10) as shown in TABLE 6.

TABLE 6 Expanded Substituted Metalloporphyrins

(31)

(32)

where each R¹ is independently —H; —X, where X is a halogen atom; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, where R can include, butnot be limited to, any identical or different, linear or branched,C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or a combination thereof,and Z can be one or more heteroatom selected from N, O, P, S, Se, or Si;—ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX, —RC(O)NH₂, —RC(O)NR,—RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, or any combinationthereof, where R can include, but is not to be limited to, any identicalor different, linear, branched, or cyclic C₁-C₅ alkyl, C₁-C₅₀ alkenyl,C₁-C₅₀ alkynyl, or a combination thereof, or can be absent such that theremaining portion of the functional group is covalently bound directlyto one or more carbon atoms of the expanded substitutedmetalloporphyrin; and

where R² is independently —H; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR,—ZRZR, or —RZRZR, where R can include, but not be limited to, anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and

where every R¹ and R² group is covalently bound directly to the expandedsubstituted metalloporphyrin; and

where M is a metal including but not limited to aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and where the oxidation stateof the metal can include, but not be limited to an oxidation state of I,II, III, IV, V, VI, VII, or VIII. In some embodiments, the metal ismagnesium. In some embodiments the metal is silver. In some embodimentsthe metal is platinum. In some embodiments the metal is palladium. Insome embodiments the metal is zinc. In some embodiments, variousinorganic, organic, ionic, or neutral ligands can be coordinated withthe metals herein, including, but not to be limited to, Cl⁻, F⁻, Br⁻,I⁻, CN⁻, SCN⁻, CO, NH₃, H₂O, NO, CH₃NH₂, pyridine, and the like. In someembodiments, the number of ligands can be from zero ligands to eightligands.

It will be appreciated that the expanded substituted metalloporphyrinring structures described herein can further include those havingphthalocyanine substitutions in the place of one or more of the pyrrolesubunits of the porphyrin ring structures of formulas (31) and (32).

The self-assembled monolayers can include those that are homogeneous andthose that are heterogeneous (e.g., they can include a layer having amixture of more than one type of substituted porphyrin and/orsubstituted metalloporphyrin). In some embodiments a self-assembledmonolayer can be monofunctional and in other embodiments aself-assembled monolayer can be bifunctional, trifunctional, etc. Insome embodiments, the self-assembled monolayer can include at leastabout 5%, 10%, 15%, 20%, 25%, 30%, 40%, or 50% of a secondary compound(or an amount falling within a range between any of these amounts),which can be any of the compounds described herein, but different than aprimary compound which accounts for the substantial balance of thecoverage of the graphene layer.

In some embodiments, the graphene layer can be disposed on the surfaceof a substrate. Substrate materials suitable for use herein can includemetals such as copper, nickel, ruthenium, platinum, iridium, and thelike, and metal oxides such as copper oxide, zinc oxide, magnesiumoxide, and the like. Substrate materials can also include silicon,quartz, sapphire, glass, ceramic, polymers, etc.

Further aspects of exemplary graphene varactors can be found in U.S.Pat. No. 9,513,244, the content of which is herein incorporated byreference in its entirety.

Contact Angle Goniometry

Contact angle goniometry can be used to determine the wettability of asolid surface by a liquid. Wettability, or wetting, can result from theintermolecular forces at the contact area between a liquid and a solidsurface. The degree of wetting can be described by the value of thecontact angle Φ formed between the area of contact between the liquidand the solid surface and a line tangent to the liquid-vapor interface.When a surface of a solid is hydrophilic and water is used as the testliquid, (i.e., a high degree of wettability), the value for Φ can fallwithin a range of 0 to 90 degrees. When a surface of a solid ismoderately hydrophilic to hydrophobic, (i.e., a medium degree ofwettability), the value for Φ for water as the test liquid can fallwithin a range of 85 to 105 degrees. When the surface of a solid ishighly hydrophobic, (i.e., a low degree of wettability), the value for Φwith water as the test liquid can fall within a range of 90 to 180degrees. Thus, a change in contact angle can be reflective of a changein the surface chemistry of a substrate.

Graphene surfaces and modifications made to graphene surfaces can becharacterized using contact angle goniometry. Contact angle goniometrycan provide quantitative information regarding the degree ofmodification of the graphene surface. Contact angle measurements arehighly sensitive to the functional groups present on sample surfaces andcan be used to determine the formation and extent of surface coverage ofself-assembled monolayers. A change in the contact angle from a baregraphene surface as compared to one that has been immersed into aself-assembly solution containing π-electron-rich molecules, can be usedto confirm the formation of the self-assembled monolayer on the surfaceof the graphene.

The types of solvents suitable for use in determining contact anglemeasurements, also called wetting solutions, are those that maximize thedifference between the contact angle of the solution on bare grapheneand the contact angle on the modified graphene, thereby improving dataaccuracy for measurements of binding isotherms. In some embodiments, thewetting solutions can include, but are not limited to, deionized (DI)water, NaOH aqueous solution, borate buffer (pH 9.0), other pH buffers,CF₃CH₂OH, and the like. In some embodiments, the wetting solutions arepolar. In some embodiments, the wetting solutions are non-polar.

Langmuir Adsorption Theory

Without wishing to be bound by any particular theory, it is believedthat according to Langmuir adsorption theory, monolayer modification ofgraphene can be controlled by varying the concentration of the adsorbatein the bulk of the self-assembly solution according to:

$\begin{matrix}{\theta = \frac{K*C}{1 + {K*C}}} & (1)\end{matrix}$

where θ is the fractional surface coverage, C is the concentration ofthe adsorbate in the bulk of the self-assembly solution, and K is theequilibrium constant for adsorption of the adsorbate to graphene.Experimentally, the surface coverage can be expressed by the change incontact angle between bare graphene and modified graphene according to:

$\begin{matrix}{\theta = \frac{{\Phi (i)} - {\Phi ({bare})}}{{\Phi \left( {{sat}.} \right)} - {\Phi ({bare})}}} & (2)\end{matrix}$

where Φ(i) is the contact angle of the modified graphene as a functionof the concentration in the self-assembly solution, Φ(bare) is thecontact angle of bare graphene, and Φ(sat.) is the contact angle ofgraphene modified with a complete monolayer of receptor molecules (i.e.,100% surface coverage or θ=1.0). Insertion of θ from eq. (2) into eq.(1) and solving for Φ(i) gives eq. (3)

$\begin{matrix}{{\Phi (i)} = {{\Phi ({bare})} + \frac{K*{C\left\lbrack {{\Phi \left( {{sat}.} \right)} - {\Phi ({bare})}} \right\rbrack}}{1 + {K*C}}}} & (3)\end{matrix}$

Thus, the experimentally observed Φ(i) values can be fitted as afunction of receptor concentration in the self-assembly solution, usingthe two fitting parameters K and Φ(sat.). Once these two parameters havebeen determined, relative surface coverages at different self-assemblyconcentrations can be predicted from eq. (1), using K.

Data can be fitted with the Langmuir adsorption model to determine theequilibrium constants for surface adsorption and the concentrations ofself-assembly solutions needed to form dense monolayers having 90% orgreater surface coverage (i.e., θ>0.9) on graphene. In some embodiments,a surface coverage of at least 90% or greater is desired. In someembodiments, a surface coverage of at least 95% or greater is desired.In some embodiments, a surface coverage of at least 98% or greater isdesired.

A representative Langmuir adsorption isotherm for the adsorption of asubstituted porphyrin to graphene is shown in FIG. 10 and described morefully in Example 4 below. The data show the relative monolayer coverage(dots) along with a fit based on Langmuir adsorption theory (solid line)for the adsorption of 5,15-bis(4-octadecyloxyphenyl)-porphyrin (herein“C₁₈,C₁₈-porphyrin”) to graphene, as determined by XPS measurements. Thelogarithm of the concentration as a function of relative surfacecoverage for the adsorption of C₁₈,C₁₈-porphyrin to graphene is shown inFIG. 11.

In the above example, the Langmuir model is used to determine K from theelemental compositions of the bare graphene and modified graphenesurfaces obtained using X-ray photoelectron spectroscopy (XPS). Insteadof using XPS data, data obtained with infrared spectroscopy or Ramanspectroscopy, or contact angle goniometry can also be used.

X-Ray Photoelectron Spectroscopy

X-ray photoelectron spectroscopy (XPS) is a highly sensitivespectroscopic technique that can quantitatively measure the elementalcomposition of a surface of a material. The process of XPS involvesirradiation of a surface with X-rays under a vacuum, while measuring thekinetic energy and electron release within the top 0 to 10 nm of amaterial. Without wishing to be bound by any particular theory, it isbelieved that XPS can be used to confirm the presence of aself-assembled monolayer formed on the surface of graphene.

The surface concentrations of the types of atoms that the monolayer,graphene, and the underlying substrate consist of (as determined fromXPS) depends on the Langmuir theta value of the monolayer or, in otherwords, the surface density of the monolayer molecules on the graphene.For example, the surface concentrations of carbon, oxygen, and copper(i.e., C %, O %, and Cu %, as determined from XPS) for the monolayers ofany given cyclodextrin on a copper substrate depends on theconcentration of that cyclodextrin in the self-assembly solution. Due toexperimental error, a slightly different value of the equilibriumconstant, K, for surface adsorption will result when either the C %, O%, or Cu % data are fitted separately. However, because the C %, O %, orCu % data characterize the same equilibrium, there is only one truevalue for K. Therefore, the XPS data can not only be fitted separatelyfor the C %, O %, and Cu % data but also as one combined set of data.Fitting of the combined data for several types of atoms that themonolayer, graphene, and the underlying substrate consist of gives moreaccurate estimates of the true value of K. For this purpose, thefollowing equation can be used, where each data point consists of avector comprising (i) an index, (ii) the concentration of theself-assembly solution, and (iii) the carbon, oxygen, or copperconcentration as determined by XPS.

${{{KroneckerDelta}\left\lbrack {1 - {index}} \right\rbrack}*\left\{ {{C\mspace{14mu} \% \; ({bare})} + \frac{K*{Conc}*\left\lbrack {{C\mspace{14mu} \% \; \left( {{sat}.} \right)} - {C\mspace{14mu} \% \; ({bare})}} \right\rbrack}{1 + {K*{Conc}}}} \right\}} + {{{KroneckerDelta}\left\lbrack {2 - {index}} \right\rbrack}*\left\{ {{O\mspace{14mu} \% \; ({bare})} + \frac{K*{Conc}*\left\lbrack {{O\mspace{14mu} \% \; \left( {{sat}.} \right)} - {O\mspace{14mu} \% \; ({bare})}} \right\rbrack}{1 + {K*{Conc}}}} \right\}} + {{{KroneckerDelta}\left\lbrack {3 - {index}} \right\rbrack}*\left\{ {{{Cu}\mspace{14mu} \% \; ({bare})} + \frac{K*{Conc}*\left\lbrack {{{Cu}\mspace{14mu} \% \; \left( {{sat}.} \right)} - {{Cu}\mspace{14mu} \% \; ({bare})}} \right\rbrack}{1 + {K*{Conc}}}} \right\}}$

The index 1 was used for the C % data, 2 for the 0% data, and 3 for theCu % data. The output of the Kronecker delta for the input of 0 is 1,and it is 0 for any other input. This fitting procedure provides in onestep the maximum surface concentrations of carbon, oxygen, and copper(i.e., C % (sat.), O % (sat.), and Cu % (sat.), respectively) along withone single value for K for all three adsorption isotherms.

In the example above, the K value is fitted from 3 adsorption isotherms,that is, the surface concentrations of 3 types of atoms. The same typeof fit may also be performed for adsorption isotherms of 1, 2, 3, 4, 5,6, 7, 8, 9, 10, or more different types of atoms.

The equilibrium constant K, as determined by the fit of the XPS data,can be used in the Langmuir adsorption model to determine the 0 valuefor graphene surfaces modified with various molecules forming monolayerson graphene, such as substituted porphyrins, substitutedmetalloporphyrins, and their derivatives. A representative Langmuiradsorption isotherm for the adsorption of graphene modified withC₁₈,C₁₈-porphyrin is shown in FIG. 10 and described in more detail inExample 4.

Aspects may be better understood with reference to the followingexamples. These examples are intended to be representative of specificembodiments, but are not intended as limiting the overall scope ofembodiments herein.

EXAMPLES Example 1: Synthesis of5,15-bis(4-octadecyloxyphenyl)-porphyrin

The substituted 5,15-bis(4-octadecyloxyphenyl)-porphyrin (herein“C₁₈,C₁₈-porphyrin”) was synthesized according to the reaction schemeshown in FIG. 9.

Briefly, 150.0 mg of 2,2′-dipyrrolmethane and 384.4 mg of4-octadecyloxybenzaldehyde were added to a 250 mL 2-neck round bottomflask, and the flask was vacuumed and refilled with N₂ gas three times.100 mL of anhydrous dichloromethane (CH₂Cl₂) was degassed with N₂ for 15min and then transferred to the round bottom flask. 50 μL oftrifluoroacetic acid (TFA) was then added to the round bottom flaskusing a syringe, and the mixture was stirred at room temperature in thedark for 15 h under N₂ protection. After incubation overnight, 515.2 mgof 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) was added to themixture, and the reaction was left to proceed for 3 h. The reaction wasstopped by the addition of 2 mL of triethylamine. The product solutionwas passed through an alumina column, and solvents were allowed toevaporate. The remaining solid product was purified via chromatographyon silica using CH₂Cl₂ as the eluent (R_(f)=1), followed byrecrystallization in MeOH/CH₂Cl₂, giving a purple solid. The following¹H NMR (6, ppm, CD₂Cl₂) results were obtained: 10.38 (s, 2H, —C═H), 9.48(d, 4H, aromatic H), 9.18 (d, 4H, aromatic H), 8.23 (d, 4H, aromatic H),7.41 (d, 4H, aromatic H), 4.33 (t, 4H, —OCH₂—), 2.06 (tt, 4H, —CH₂—),1.69 (tt, 4H, —CH₂—), 1.30 (m, 56H, —CH₂—), 0.91 (t, 6H, —CH₃), −3.08(s, 2H, —NH—). Mass spectrometry (MALDI, 25 mM 2,5-dihydroxybenzoic acidas matrix) results were: m/z: 999.6 (C₁₈,C₁₈-porphyrin⋅H⁺). Elementalanalysis of the solid was as follows: calculated C, 81.71%; H, 9.48%; N,5.61%. observed C, 81.86%; H, 9.55%; N, 5.63%.

Example 2: Graphene Surface Modification with C₁₈,C₁₈-porphyrin

Graphene substrates were immersed overnight into self-assembly solutionscontaining chlorobenzene and the C₁₈,C₁₈-porphyrin construct (SeeExample 1) at various concentrations (0, 0.03, 0.10, 1.0, or 3.0 mM)using chlorobenzene as the solvent. The modified graphene substrateswere washed 3 times with small portions of chlorobenzene to removeexcess self-assembly solution.

Suitable graphene substrates for use in creating self-assembledmonolayers include monolayer graphene on Cu foil as purchased fromGraphenea (Donostia, Spain) and monolayer graphene as grown on25-μm-thick Cu foils (No. 46365, Alfa Aesar, Tewksbury, Mass.) bychemical vapor deposition using hydrogen and methane flow rates of 21standard cubic centimeter per minute (sccm) and 0.105 sccm,respectively, at 1050° C.

Example 3: XPS of Bare Graphene

X-ray photoelectron spectroscopy (XPS) spectra of bare graphene on acopper substrate were collected on a VersaProbe III Scanning XPSMicroprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). Theobserved elemental surface composition of bare graphene on a coppersubstrate was found to be 57.1 mol % carbon, 12.7 mol % oxygen, and 30.2mol % copper, as shown in TABLE 7.

Example 4: XPS of Graphene Modified with C₁₈,C₁₈-porphyrin

XPS of graphene modified with C₁₈,C₁₈-porphyrin was performed todetermine the Carbon % (C %), Oxygen % (O %), and Copper % (Cu %) of themodified surface. The XPS spectra were collected on a VersaProbe IIIScanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen,Minn.).

The results for the elemental surface composition of graphene modifiedwith C₁₈,C₁₈-porphyrin are shown in TABLE 7. The Langmuir adsorptionisotherm for the adsorption of graphene modified with C₁₈,C₁₈-porphyrinis shown in FIG. 10. The data show the relative monolayer coverage(dots) along with a fit (solid line) based on Langmuir adsorption theoryfor the adsorption of graphene modified with C₁₈,C₁₈-porphyrin, asdetermined by XPS data. The relative surface coverage for the adsorptionof C₁₈,C₁₈-porphyrin to graphene as a function of the logarithm of theC₁₈,C₁₈-porphyrin concentration in the self-assembly solution is shownin FIG. 11.

TABLE 7 Elemental surface composition of graphene modified withC₁₈,C₁₈-porphyrin, as determined by XPS C₁₈,C₁₈-porphyrin Concentration(mM) in self-assembly solution C % Cu % O % 0 57.1 ± 1.4 30.2 ± 2.7 12.7± 1.4 0.03 58.3 ± 0.6 29.5 ± 2.0 12.2 ± 2.2 0.10 59.8 ± 1.7 25.3 ± 2.814.8 ± 1.1 1.0 62.0 ± 0.7 23.7 ± 1.7 14.2 ± 1.2 3.0 62.0 ± 0.5 25.9 ±1.0 12.2 ± 0.6

The C % and Cu % data were fitted simultaneously, as described above, todetermine the equilibrium constant K. The O % data were not includedinto the fitting because the maximum change in O % fell within thebackground noise of the experiment. The equilibrium constant, K, andconcentration of self-assembly solution needed for at least 90%monolayer formation with C₁₈,C₁₈-porphyrin are shown in TABLE 8.

TABLE 8 Equilibrium constants and monolayer concentrations foradsorption of C₁₈,C₁₈-porphyrin on graphene Concentration ofself-assembly solution needed for Self-Assembly Log K Self-assembly 90%surface Molecule (Log M⁻¹) solvent coverage (mM) C₁₈,C₁₈-porphyrin 4.18chlorobenzene 0.6 (3.90-4.35)

Further, modification of graphene with C₁₈,C₁₈-porphyrin can beconfirmed by the presence of nitrogen in the N1s XPS spectrum. The N1sXPS spectrum for graphene modified with C₁₈,C₁₈-porphyrin reveals an N1speak at approximately 399.6 eV (FIG. 12). In contrast, the N1s XPSspectrum for bare graphene reveals no peaks for nitrogen at or nearapproximately 400 eV (FIG. 13).

Example 5: Synthesis of Zn(II) 5,15-bis(4-octadecyloxyphenyl)porphyrin

The substituted Zn(II) 5,15-bis(4-octadecyloxyphenyl)porphyrin (herein“Zn(II) C₁₈,C₁₈-Zn(II)porphyrin”) was synthesized.

Briefly, 32.0 mg of C₁₈,C₁₈-porphyrin and 70.3 mg of Zn(II) acetatedihydrate were dissolved in 5 mL anhydrous dimethyl formamide and themixture was refluxed for 24 h under the protection of N₂. After the 24hr incubation period, 10 mL of water was added to the mixture to form aprecipitate. The precipitate was collected, washed with water, andrecrystallized in CH₂Cl₂. The following ¹H NMR (6, ppm, CD₂Cl₂) resultswere obtained: 10.40 (s, 2H, —C═H), 9.53 (d, 4H, aromatic H), 9.24 (d,4H, aromatic H), 8.22 (d, 4H, aromatic H), 7.39 (d, 4H, aromatic H),4.34 (t, 4H, —OCH₂—), 2.05 (tt, 4H, —CH₂—), 1.67 (tt, 4H, —CH₂—), 1.30(m, 56H, —CH₂—), 0.92 (t, 6H, —CH₃). Mass spectrometry (MALDI, 25 mM2,5-dihydroxybenzoic acid as matrix) results were: m/z: 1060.6 (Zn(II)C₁₈,C₁₈-porphyrin⋅H⁺).

It should be noted that, as used in this specification and the appendedclaims, the singular forms “a,” “an,” and “the” include plural referentsunless the content clearly dictates otherwise. Thus, for example,reference to a composition containing “a compound” includes a mixture oftwo or more compounds. It should also be noted that the term “or” isgenerally employed in its sense including “and/or” unless the contentclearly dictates otherwise.

It should also be noted that, as used in this specification and theappended claims, the phrase “configured” describes a system, apparatus,or other structure that is constructed or configured to perform aparticular task or adopt a particular configuration to. The phrase“configured” can be used interchangeably with other similar phrases suchas arranged and configured, constructed and arranged, constructed,manufactured and arranged, and the like.

All publications and patent applications in this specification areindicative of the level of ordinary skill in the art to which thisinvention pertains. All publications and patent applications are hereinincorporated by reference to the same extent as if each individualpublication or patent application was specifically and individuallyindicated by reference.

The embodiments described herein are not intended to be exhaustive or tolimit the invention to the precise forms disclosed in the followingdetailed description. Rather, the embodiments are chosen and describedso that others skilled in the art can appreciate and understand theprinciples and practices. As such, aspects have been described withreference to various specific and preferred embodiments and techniques.However, it should be understood that many variations and modificationsmay be made while remaining within the spirit and scope herein.

1. A medical device comprising: a graphene varactor comprising: agraphene layer; a self-assembled monolayer disposed on an outer surfaceof the graphene layer through electrostatic interactions between apartial positive charge on hydrogen atoms of one or more hydrocarbons ofthe self-assembled monolayer and a π-electron system of graphene; andwherein the self-assembled monolayer comprises one or more substitutedporphyrins or substituted metalloporphyrins, or derivatives thereof. 2.The medical device of claim 1, wherein the self-assembled monolayerprovides a Langmuir theta value of at least 0.9.
 3. The medical deviceof claim 1, wherein the self-assembled monolayer provides a Langmuirtheta value of at least 0.98.
 4. The medical device of claim 1, whereinthe self-assembled monolayer provides coverage over the graphene from50% to 150% by surface area.
 5. The medical device of claim 1,comprising a plurality of graphene varactors configured in an array onthe medical device.
 6. The medical device of claim 1, the self-assembledmonolayer comprising substituted porphyrins of the formula:

wherein each R¹ functional group independently comprises: —H; —X,wherein X comprises a halogen atom; any linear or branched C₁-C₅₀ alkyl,C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR,—ZRZR, or —RZRZR, wherein R comprises any identical or different, linearor branched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or anycombination thereof, and Z can be one or more heteroatom selected fromN, O, P, S, Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX,—RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, orany combination thereof, wherein R comprises any identical or different,linear, branched, or cyclic C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or a combination thereof, or is absent such that the remainingportion of the functional group is covalently bound directly to one ormore carbon atoms of the substituted porphyrin; and wherein each R² andR³ functional group independently comprises: —H; any linear or branchedC₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀heteroalkenyl, C₁-C₅₀ heteroalkynyl or any combination thereof; —RZR or—RZRZR, wherein R comprises any identical or different, linear orbranched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or anycombination thereof, and Z can be one or more heteroatom selected fromN, O, P, S, Se, or Si; an aryl, heteroaryl, substituted aryl, orsubstituted heteroaryl; a biphenyl or substituted biphenyl; an aryloxy,arylthio, arylamine, or any substitutions thereof; or any combinationthereof; and wherein R¹, R², and R³ are each covalently bound directlyto the substituted porphyrin.
 7. The medical device of claim 6, whereinR² and R³ are different.
 8. The medical device of claim 6, each alkyl,alkenyl, alkynyl, heteroalkyl, heteroalkenyl, or heteroalkynylindependently comprising any linear or branched hydrocarbon functionalgroup having from 6 to 32 carbon atoms.
 9. The medical device of claim1, the self-assembled monolayer comprising substituted porphyrins of theformula:

wherein each X is independently a heteroatom comprising N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; and wherein each R functional group independently comprises: —H;any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl,C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, wherein R comprises anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof.
 10. The medicaldevice of claim 1, the self-assembled monolayer comprising substitutedporphyrins of the formula:


11. The medical device of claim 1, the self-assembled monolayercomprising substituted metalloporphyrins of the formula:

wherein each R¹ functional group independently comprises —H; —X, whereinX comprises a halogen atom; any linear or branched C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀ heteroalkyl, C₁-C₅₀ heteroalkenyl,C₁-C₅₀ heteroalkynyl, or any combination thereof; —RZR, —ZRZR, or—RZRZR, wherein R comprises any identical or different, linear orbranched, C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, or anycombination thereof, and Z can be one or more heteroatom selected fromN, O, P, S, Se, or Si; —ROH, —RC(O)OH, —RC(O)OR, —ROR, —RSR, —RCHO, —RX,—RC(O)NH₂, —RC(O)NR, —RNH₃ ⁺, —RNH₂, —RNO₂, —RNR, —RNRR, —RB(OH)₂, orany combination thereof, wherein R comprises any identical or different,linear, branched, or cyclic C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀alkynyl, or a combination thereof, or is absent such that the remainingportion of the functional group is covalently bound directly to one ormore carbon atoms of the substituted metalloporphyrin; wherein each R²and R³ functional group independently comprises: —H; any linear orbranched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, wherein R comprises anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; wherein R¹, R², andR³ are each covalently bound directly to the substitutedmetalloporphyrin; and wherein M is a metal comprising aluminum, calcium,magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium,silver, platinum, indium, tin, copper, rhodium, chromium, gallium,osmium, iridium, or derivatives thereof; and wherein an oxidation stateof the metal can include, but not be limited to I, II, III, IV, V, VI,VII, or VIII.
 12. The medical device of claim 11, wherein R² and R³ aredifferent.
 13. The medical device of claim 1, the self-assembledmonolayer comprising substituted metalloporphyrins of the formula:

wherein each X is independently a heteroatom comprising N, O, P, S, Se,or Si, or absent, such that R is covalently attached to the phenylgroup; wherein each R functional group independently comprises: —H; anylinear or branched C₁-C₅₀ alkyl, C₁-C₅₀ alkenyl, C₁-C₅₀ alkynyl, C₁-C₅₀heteroalkyl, C₁-C₅₀ heteroalkenyl, C₁-C₅₀ heteroalkynyl, or anycombination thereof; —RZR, —ZRZR, or —RZRZR, wherein R comprises anyidentical or different, linear or branched, C₁-C₅₀ alkyl, C₁-C₅₀alkenyl, C₁-C₅₀ alkynyl, or any combination thereof, and Z can be one ormore heteroatom selected from N, O, P, S, Se, or Si; an aryl,heteroaryl, substituted aryl, or substituted heteroaryl; a biphenyl orsubstituted biphenyl; an aryloxy, arylthio, arylamine, or anysubstitutions thereof; or any combination thereof; and wherein M is ametal comprising aluminum, calcium, magnesium, manganese, iron, cobalt,nickel, zinc, ruthenium, palladium, silver, platinum, indium, tin,copper, rhodium, chromium, gallium, osmium, iridium, or derivativesthereof; and wherein an oxidation state of the metal comprises I, II,III, IV, V, VI, VII, or VIII.
 14. A method of modifying a surface ofgraphene to create a graphene varactor, the method comprising: forming aself-assembled monolayer disposed on an outer surface of the graphenelayer through electrostatic interactions between a partial positivecharge on hydrogen atoms of one or more hydrocarbons of theself-assembled monolayer and a π-electron system of graphene; theself-assembled monolayer comprising one or more substituted porphyrinsor substituted metalloporphyrins, or derivatives thereof; andquantifying the extent of surface coverage of the self-assembledmonolayer using contact angle goniometry, Raman spectroscopy, or X-Rayphotoelectron spectroscopy.
 15. The method of claim 14, whereinselecting derivatized graphene layers includes selecting derivatizedgraphene layers that exhibit a Langmuir theta value of at least 0.9. 16.The method of claim 14, wherein selecting derivatized graphene layersincludes selecting derivatized graphene layers that exhibit a Langmuirtheta value of at least 0.98.
 17. A method for detecting an analytecomprising: collecting a gaseous sample from a patient; contacting thegaseous sample with one or more graphene varactors, each of the one ormore graphene varactors comprising: a graphene layer; a self-assembledmonolayer disposed on an outer surface of the graphene layer throughelectrostatic interactions between a partial positive charge on hydrogenatoms of one or more hydrocarbons of the self-assembled monolayer and aπ-electron system of graphene; and wherein the self-assembled monolayercomprises at least one selected from the group consisting of substitutedporphyrins or substituted metalloporphyrins, or derivatives thereof. 18.The method of claim 17, further comprising measuring a differentialresponse in an electrical property of the one or more graphene varactorsdue to the binding of one or more analytes present in the gaseoussample.
 19. The method of claim 18, the electrical property selectedfrom the group consisting of capacitance or resistance.
 20. The methodof claim 17, wherein the self-assembled monolayer provides a Langmuirtheta value of at least 0.9.